In order to measure flow in very narrow channels such as blood vessels, it has been known for a long time to employ a number of different methods, e.g. the so called timed venous collection technique, electromagnetic flow measurements, epicardial ultrasonic flow velocity measurement, the thermo-dilution technique, and other techniques. For details on these techniques, reference is made to "Maximal Myocardial Perfusion as a Measure of the Functional Significance of Coronary Artery Disease", by N. H. J. Pijls, (1991), Cip-Gegevens Koninklijke Bibliotheek, den Haag, (ISBN 90-9003818-3).
The present invention concerns improvements in the operation of the thermodilution principle, and therefore this principle will be briefly summarized below.
Application of the thermodilution principle in the coronary sinus was introduced by Ganz (Ganz et al, "Measurement of coronary sinus blood flow by continuous thermodilution in man, Circulation 44:181-195, 1971). A small catheter is introduced deeply into the coronary sinus and cold saline is delivered at its tip. Theoretically, flow can be calculated from the changes in blood temperature, registered by a thermistor close to the outlet of the coronary sinus. An advantage of this method is that only right heart catheterization is required.
The principle of thermo-dilution involves injecting a known amount of cooled liquid, e.g. physiological saline in a blood vessel. After injection the temperature is continuously recorded with a temperature sensor attached to the tip of a guide wire that is inserted in the vessel. A temperature change due to the cold liquid passing the measurement site, i.e. the location of the sensor, will be a function of the flow.
There are various methods of evaluating the temperature signal for diagnostic purposes. Either one may attempt to calculate the volume flow, or one may use a relative measure, where the flow in a "rest condition" is compared with a "work condition", induced by medicaments.
The latter is the simpler way, and may be carried out by measuring the width at half height of the temperature change profile in the two situations indicated, and forming a ratio between these quantities.
Another way of obtaining a ratio would be to measure the transit time from injection and until the cold liquid passes the sensor, in rest condition and in work condition respectively.
The former method, i.e. the utilization of the volume flow parameter as such, requires integration of the temperature profile over time in accordance with the equations given below: ##EQU1## wherein V is the volume of injected liquid
T.sub.r,m is the measured temperature at rest condition PA1 T.sub.r,l is the temperature of injected liquid at rest condition PA1 T.sub.0 is the temperature of the blood, i.e. 37.degree. C. PA1 T.sub.w,m is the measured temperature at work condition PA1 T.sub.w,l is the temperature of injected liquid at work condition PA1 Q is the volume flow
These quantities may be used directly for assessment of the condition of the coronary vessels and the myocardium of the patient, or they may be ratioed as previously to obtain a CFR, i.e. CFR=Q.sub.work /Q.sub.rest.
The latter method, i.e. determination of the transit time requires an accurate time measurement, in view of the relatively small distances in question, about 10 cm or less from injection to measurement site.
E.g. in order to obtain a correct measurement, the time has to be measured with some accuracy. Using a simple stop watch, which is a common means of timing, is far too inaccurate for obtaining reliable transit times.
The flow F may be obtained as follows, which is a derivation for a similar technique, namely the indicator dilution technique. This is based on a rapidly injected amount of some kind of indicator, the concentration of which is measured.
For this purpose, the function h(t) is introduced which is the fraction of indicator, passing per unit of time at a measurement site at time t. In other words, h(t) is the distribution function of transit times of the indicator particles. If it is assumed that that flow of the indicator is representative for flow of the total fluid (complete mixing), h(t) is also the distribution function of transit times of all fluid particles. Suppose the total volume of fluid is made up of a very large number of volume elements dV.sub.i which are defined in such a way that dV.sub.i contains all fluid particles present in the system at t=0, with transit times between t.sub.i and t.sub.i+1. The fraction of fluid particles requiring times between t.sub.i and t.sub.i+1, to pass the measurement site, is h(t.sub.i).multidot..DELTA.t by definition, and because the rate at which the fluid particles pass at the measurement site, equals F, the rate at which the particles making up dV.sub.i pass at the measurement site is F.multidot.h(t.sub.i).multidot..DELTA.t. The total volume of dV.sub.i equals the time t.sub.i, required for all particle segments in dV.sub.i to pass at the measurement site multiplied by the rate at which they leave. In other words: EQU dV.sub.i =t.sub.i .multidot.F.multidot.h(t.sub.i).multidot..DELTA.t
and by integration: ##EQU2##
The integral in the equation above represents the mean transit time T.sub.mn, which is the average time, needed by one particle to travel from an injection site to a measurement site. Therefore: EQU V=F.multidot.T.sub.mn
or: EQU F=V/T.sub.mn ; T.sub.mn =V/F
which states the fundamental fact that flow equals volume divided by mean transit time.
Although the above derivation was made for the mentioned indicator dilution technique, the result is the same for thermo-dilution since the same distribution function may be employed.